Blind Channel Estimation

ABSTRACT: Multiple-Input Multiple-Output (MIMO) technology is becoming nature for wireless communications. This Paper presents to the Blind channel estimation of Massive MIMO, And it has been incorporated into wireless broadband standards like LTE and Wi-Fi. It allows the use of multiple antennas at the transmitter and the receiver to increase the data rate, capacity and the link reliability. Multiple antennas at the transmitter and the receiver are used to exploit the multipath propagation. One of the key techniques that enable MIMO is Orthogonal Frequency Division Multiplexing (OFDM). In OFDM, the multiple symbols are transmitted in parallel on the same frequency band. Each symbol is transmitted sequentially in a narrow frequency band for a greater period of time which enables the receiver to pull each symbol. Even if the symbol is degraded, it is possible to receive one of the best symbol for the fact that it is been transmitted for a longer duration which is important while working in MIMO environment. By using OFDM technique the spectral efficiency can be improved and also by using more number of antennas the overall efficiency of the system can be increased.

should be able to recover the data i.e effective channel estimation is essential. Basically it is done to know or to predict the behaviour of wireless channel. We add extra bits with the data bits to know the behaviour of the channel these bits are called pilots. Now, it is achieved by using dedicated pilot symbols which consume a non negligible part of the throughput and power resources especially for large dimensional systems. The main objective of this paper is to quantify the rate of reduction of this overhead due to the use of a semi-blind channel estimation. Different data models and different pilot design schemes have been considered in this study. By using the Cramér Rao Bound (CRB) tool, the estimation error variance bounds of the pilot-based and semi-blind based channel estimators for a Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system are compared. In particular, for large MIMO-OFDM systems, a direct computation of the CRB is prohibitive and hence a dedicated numerical technique for its fast computation has been developed. Many key observations have been made from this comparative study. The most important one is that, thanks to the semi-blind approach, one can skip about 95% of the pilot samples without affecting the channel estimation quality.

We propose a statistical covariance-matching based blind channel estimation scheme for zero-padding (ZP) multiple- input multiple-output (MIMO)–orthogonal frequency division multiplexing (OFDM) systems. By exploiting the block Toeplitz channel matrix structure, it is shown that the linear equations relating the entries of the received covariance matrix and the outer product of the MIMO channel matrix taps can be rearranged into a set of decoupled groups. The decoupled nature reduces computations, and more importantly guarantees unique recovery of the channel matrix outer product under a quite mild condition. Then the channel impulse response matrix is identified, up to a Hermitian matrix ambiguity, through an eigen-decomposition of the outer product matrix. Simulation results are used to evidence the advantages of the proposed method over a recently reported subspace algorithm applicable to the ZP-based MIMO–OFDM scheme.

These previously reported methods, however, require a large amount of received data to ob- tain accurate statistics for successful block synchronization. As we examine these previously re- ported blind block synchronization algorithms, we find that block synchronization algorithms can be connected with existing blind channel estimation/equalization algorithms that exploit matrix null spaces. In recent years, more advanced blind channel estimation algorithms, including those presented in Chapters 2 and 3, were developed. These suggest more opportunities to develop new blind channel synchronization algorithms that may possess new features. The feature of using much less received data in the blind channel estimation algorithms can also be properly transferred to blind synchronization algorithms if we adopt the concept of repetition index. The blind block synchronization algorithm for ZP systems proposed in this chapter will explore this idea. Another novelty is that the proposed method for ZP systems is based on a subspace of dimension L rather than one as in [45] (where L is the channel order). This idea, combined with the repetition index, is shown to significantly improve the performance with sufficient amount of received data. As for CP systems, our approach to reduce the required amount of received data resorts to employing the idea of repetition index. As the idea of repetition index was recently extended to blind chan- nel estimation in CP systems [60], we propose a new blind block synchronization algorithm in CP systems based on the foundation of [60]. Our proposed algorithm possesses two advantages over the previously reported methods: 1) In absence of noise, the proposed algorithm provides correct recovery of block boundaries using only three received blocks, whereas all previously reported al- gorithms require the number of received blocks to be no less than the block size. 2) When noise is present, simulation results as reported in Section 4.5 show that given the same amount of received data, the proposed algorithm has an obvious improvement in blind block synchronization error rate performance over the previously reported algorithm in [33].

the need for a training sequence numerous. This motivates the development of receiver structures with blind channel estimation capabilities. There has been considerable work reported in the literature on the estimation of channel in- formation to improve performance of space-time coded sys- tems operating on fading channels [4, 5, 6, 7]. In this paper, we consider the problem of blind estimation of space-time coded signals along with the matrix of path gains. We pro- pose two different approaches based on the assumptions on the input sequences. Our proposed approaches also exploit the finite alphabet property of the space-time coded sig- nals. We treat both conditional and unconditional maximum likelihood (ML) approaches. The first approach (conditional ML) results in joint estimation of the channel matrix and the input sequences, and is based on the iterative least squares and projection [8]. The second approach, which is known as unconditional ML, treats the input sequence as stochastic in- dependent identically distributed (i.i.d.) sequences. In con- trast, the unconditional ML approach formulates the blind estimation problem in discrete-time finite state Markov pro- cess framework [9, 10, 11]. Since the proposed algorithms obtain ML estimates of channel matrix and the space-time coded signals, they enjoy many attractive properties of the ML estimator including consistency and asymptotic normal- ity. Moreover, it is asymptotically unbiased and its error co- variance approaches Cram´er-Rao lower bound (CRB).

In this paper, a blind channel estimation technique for multiple-input multiple-output (MIMO) space-time block coded (STBC) systems has been proposed. The technique is solely based on second-order statistics (SOS), and its computational complexity reduces to the extraction of the principal eigenvector of a generalized eigenvalue problem (GEV). In the absence of noise it exactly recovers the channel, up to a real scalar, within a finite number of observations, that is, it is a deterministic technique. Additionally, it has been shown that the ambiguity problems associated to certain STBCs are due to the code structure, and not to the proposed channel estimation algorithm. Furthermore, we have proposed a general method to avoid the ambiguities, which is based on the idea of code combination. As a partic- ular case, this technique can be reduced to a nonredundant precoding of the transmitted signals, consisting of a single rotation or permutation of the transmit antennas. Finally, the proposed technique has been evaluated by means of numerical examples, showing that, for a su ffi ciently large number of observations, its performance is close to that of the coherent receivers.

Space-time coded systems, which generally fall into the MIMO framework, bring significant challenges to channel identification. In fact, in order to fully exploit the space-time diversity, the channel state information generally needs to be estimated for all possible paths between the transmitter and receiver antenna pairs. Training-based channel estimation may result in considerable overhead. To further increase the spectral efficiency of space-time coded system, blind chan- nel identification and signal detection algorithms have been proposed. In [24], blind and semiblind equalizations, which exploit the structure of space-time coded signals, are pre- sented for generalized space-time block codes which employ redundant precoders. Subspace-based blind and semiblind approaches have been presented in [25–28], and a family of convergent kurtosis-based blind space-time equalization techniques is examined in [29]. Blind algorithms based on the MUSIC and Capon techniques can be found in [30, 31], for example. Blind channel estimation for orthogonal space- time block codes (OSTBCs) has also been explored in liter- ature, see [32–34], for example. In [33], based on specific properties of OSTBCs, a closed-form blind MIMO chan- nel estimation method was proposed, together with a simple precoding method to resolve possible ambiguity in channel estimation.

Abstract – Channel Estimation (CE) in multicarrier system especially in Orthogonal Frequency Division Multiplexing (OFDM) systems has become an important technique in wireless communication to reduce the overall effect of high data rate and increase links performance. In wireless channel, which has frequency selective distribution, the transmitted signals are corrupted and resulted in high error at the receiver. However, the existing techniques in use such as Least Square Estimation (LSE), Minimum Mean Square Error (MMSE) are based on single carrier system with pilot symbols for channel estimation to reduce the error. Therefore, in this paper, investigation of the performance of blind channel estimation in sixteen (16) subcarriers OFDM system using a Constant Modulus Algorithm (CMA) is carried out. The system model for sixteen subcarriers OFDM incorporating CMA is developed over the frequency selective fading channel. OFDM system consists of the following signal processing techniques; sixteen channel demultiplexer, Inverse Fast Fourier transform (IFFT), Cyclic Prefix (CP), sixteen channels multiplexer and the Radio Frequency (RF) transmit antenna all at the transmitter. Also, at the receiver are RF receive antenna, sixteen channel demultiplexer, Fast Fourier transform (FFT), sixteen channel multiplexer, Cyclic Prefix (CP) removal and decoder. The input data are generated randomly, converted to bits and divided among the subcarriers to reduce overlapping of bits. The signal processing techniques at both the transmitter and receiver process the signal. The system model is simulated by MATLAB application package and evaluated using Mean Square Error (MSE). This is now compared with the LSE and MMSE estimation. The results obtained using 16- subcarrier OFDM with CMA give lower MSE than with LSE over frequency selective environment.

Several SBCE solutions have been proposed to minimize the computational cost, and hence the energy spent in channel estimation of MIMO systems. The SBCE schemes suggested in [8] [9] use few training symbols to provide initial estimate and then the data detector and estimator exchange the information iteratively. In [10] [11] and [12] the MIMO channel matrix is decomposed into whitening and rotation matrix. The whitening matrix is estimated using blind symbols and the rotation matrix is estimated using few orthogonal pilot symbols. This Orthogonal Pilot Maximum Likelihood (OPML) estimator shows a 1dB improvement of bit error rate (BER) compared to the conventional least squares (LS) training scheme if the same length of training sequence is used. Furthermore, SVD has to be applied twice to obtain the ‘whitening’ matrix and the rotation matrix. These operations lead to the increased computational complexity [12]. The authors feel that the semi-blind method with QR decomposition suggested in [12] is not mathematically correct and hence it is impossible to implement. Moreover the improvement suggested in [12] over the SVD-OPML method assumes knowledge of transmitted symbols at the receiver which is practically infeasible. Because of the assumption of at receiver the authors of [12] are successful in getting near optimal performance.A signal perturbation free whitening rotation based semi blind channel estimation is discussed in [14]. In [15] TBCE and SBCE, considering Perfect, LS, LMMSE, ML, and MAP estimators are studied in terms of BER and complexity. Subspace based semi-blind channel estimation is discussed in [17] [18].A linear prediction based semi-blind estimation for FIR MIMO channel is proposed in [18]. Number of semi-blind channel estimation schemes are reported for OFDM and MIMO-OFDM systems as well [19]- [26].

In this thesis, subspace-based techniques have been successfully applied to blind chan- nel estimation and multiuser detection for multi-rate DS/CDMA. However, as stated in Section 1.3, the computational complexity of subspace-based approaches is usually pro- hibitively high, since they typically require not only a long duration of observation, but also some form of eigen-decomposition. Moreover, the channel is often required to be time-invariant during this long observation period, which potentially makes these algo- rithms impractical for wireless communications. Recently, there has been some interest in semi-blind methods for single-rate systems [32], [111], which exploit the statistics of the unknown data as well as the known pilot signal, and require a shorter duration of obser- vation to achieve the same performance as the blind methods. As a result, the study on semi-blind channel estimation and multiuser detection for multi-rate DS/CDMA is very promising and should become a major area for further study.

Blind estimation or detection algorithms have been pro- posed for space-time coded CDMA systems. For example, a blind channel estimation technique based on the Capon re- ceiver or the minimum output variance technique for flat fading channels, with two spreading codes per user, was pro- posed in [16]. In this paper, we propose a blind channel es- timation technique for frequency-selective fading channels, with a single spreading code per user. The proposed method requires no more than two pilot symbols per user per slot. (This is the same number of pilot symbols as in di ff eren- tial detection schemes.) The proposed algorithm exploits the subspace structure of the long code WCDMA transmission and the orthogonality of the unitary codes, for example, the Alamouti code. As a subspace technique, the proposed al- gorithm is based on the front-end processing, and requires the code matrix to be invertible in the case of the decorre- lating front ends. The proposed method can obtain chan- nel estimates quickly using only one slot, which allows us to deal with rapidly fading channels. Using a rake structure, our technique is compatible with the standard receiver front ends that suppress multiaccess interference, and perform decod- ing for each user separately.

Extensive computer simulations have been conducted to demonstrate and compare the performance of Training based LS, WR based semi-blind channel estimation and proposed novel semi-blind channel estimation techniques for Rayleigh flat fading MIMO channels. We consider alamouti coded 2 × 6 (two transmitters and six receivers) MIMO systems with 100 blind data symbols among 20,000 pair transmitted symbols under 4-PSK modula- tion scheme using 4, 8 and 16 pilot symbols. Result shows in figures depicts that semi-blind channel estima- tion techniques have better BER performance than train- ing based LS channel estimation technique further first novel technique with perfect R outperforms others. 4.1. BER (Bit Error Rate)

Tx1 and Tx2, respectively. A trade-off is often made be- tween the bandwidth allocated to an MC-CDMA system and the processing gain P such that Q is an integer mul- tiple of P [11]. Here, we assume that P = Q to simplify the presentation; in the event that Q > P, multiple user symbols can be spread and transmitted across the entire system bandwidth simultaneously [11]. After spreading, the IFFT of the spread signal is computed (to perform OFDM modulation) along with CP insertion. Finally, the STC-MC- CDMA signal is parallel-to-serial (P/S) converted and sent out by the two Tx’s. At the receiver, the received signal is first serial-to-parallel (S/P) converted and followed by CP removal and FFT (to perform OFDM demodulation). The FFT processor outputs are then weighted and combined to generate decision variables by utilizing channel estimates ob- tained by either some training or blind channel estimation scheme.

Usually the radio signals are highly dynamic, where the transmitted signals travel to the receiver by experiencing numerous detrimental effects, which corrupts the signals and often lessen the system performance. Channel estimation is utilized to identify the channel state information in order to understand the channel properties. This information gives details about transmitted signal from transmitter to receiver. Channel Estimation (CE) methods estimates the impulse response of the channel and also describes about the channel behavior. The CE methods are utilized to improve SNR, system performance, mobile localization, and channel equalization, and also to reduce inter symbol interference [1], [2]. Generally, CE approaches are sub-divided into two types: blind type and pilot type. CE is carried-out to investigate the channel effect on signal by inserting pilot tones into every OFDM symbol. The existing CE approaches needs probe sequence to occupy reliable bandwidth, but it utilizes only the received data. Though, the blind CE approaches are attractive compared to the trained approaches, due to self-sufficiency in training [3], [4]. The convergence rate of blind channel estimator is very slow, because it requires huge amount of data.

freedom for eigenvalue comparison. The drawback of us- ing big dimension is that the required number of sam- ples will be big too for statistical convergence of the data correlation matrix. Most EVD-based algorithms also suffer from huge computational complexity and numerical sen- sitivity due to the big dimension. Without the EVD, Ger- stacker and Taylor [14] developed a detection algorithm based on the examination of an indicator function con- structed from initial channel estimates containing an addi- tional common polynomial factor. However, its performance depends on the accuracy of the channel estimation algo- rithm.

A short cyclic prefix, rather than differential coding, isused for removing the phase ambiguity imposed by the blind channel estimation scheme, and the Akaike information theoretic crite[r]

For blind channel estimation methods, earlier works require either higher order statistics (HOS) of the received data [18] or over-sampling at the receiver [19]. By exploit- ing linear redundant precoding , only second-order statis- tics (SOS) of the received data is required and these methods are robust to channel order overestimation [20, 21]. Another popular blind algorithm is the so-called subspace-based algorithm which was originally developed in [19]. The subspace method has simple structure and achieves good performance. In [22], a blind channel iden- tification method by exploiting virtual carriers (VC) is derived. In [23], a generalization in cyclic prefix (CP) sys- tems is proposed. By arranging the received data appro- priately, [23] generates a rank-deduction matrix, and thus, subspace method can work. In [24], the authors propose another simpler arrangement of the received data. Pan and Phoong [25] and [26] utilize the repetition method to reduce the number of required received data and consider the existence of VCs.

The present channel estimation methods are divided into two types: based on the pilots and the second is the blind channel estimation which does not use pilots. Blind channel estimation methods do not use pilots and have higher spectral efficiency. Blind channel estimation methods are not suitable for applications with fast varying fading channels. The channel estimation methods which are widely used for the pilot aided channel estimation methods are divided into two types: the block type pilot channel estimation and the comb type pilot channel estimation [11]. In the block type pilot channel estimation, pilots are inserted into all the subcarriers of one OFDM symbol with a certain period and they can be adopted in slow fading channel which means the channel is static within a certain period of OFDM symbols. The comb-type refers to the pilots which are inserted at some specific subcarriers in each OFDM symbol. The comb-type is preferred in fast varying fading channel that is the channel varies over two adjacent OFDM symbols but remains static with one OFDM symbol [11]. When the fading channel cannot be viewed as a static within an OFDM symbol, then ICI occurs whereas the comb-type pilot patterns cannot eliminate ICI. There are some channel estimation methods for the pilot aided channel estimation which are LS (Least Square) and MMSE (Minimum Mean Square Estimation) [11].

High data rate transmission, spectral efficiency and reliability are necessary for future wireless communication systems. MIMO-OFDM (multiple input multiple output- orthogonal frequency division multiplexing) technology, has gained great popularity for its capability of high rate transmission and its robustness against multi-path fading and other channel impairments with the available power and bandwidth. A major challenge to MIMO-OFDM systems is how to obtain the channel state information accurately and promptly for coherent detection of information symbols and channel synchronization. When perfect knowledge of the wireless channel conditions is available at the receiver, the capacity has been shown to grow linearly with the number of antennas. In this work, MIMO-OFDM channel estimation is done by using a novel pilot signal that is well suited for wide band applications. Least Square (LS) and Minimum Mean Square error (MMSE) channel estimation methods are employed. Blind channel estimation and training sequence based estimation for fading channels (Rayleigh and Rician) using these two methods have been carried out. To improve the performance a new chaotic sequence is used for channel estimation. Finally the Mean square Error (MSE) analysis is done for SISO-OFDM and MIMO-OFDM and comparison is made between LS and MMSE methods through MATLAB simulation with chaotic pilot sequence and conventional pilot sequence. The proposed chaotic pilot sequence estimation gives superior performance.

side. In the receiver side, the multiple signals from the transmitter are reached with a group of OFDM demodulators and the CSI can be estimated by any training based algorithms. A simple diversity technique [1] was delivered with two antennas at the transmitter and one antenna at the receiver and numerous issues such as power requirements, delay effect, channel estimation errors and bit error rate performance were discussed. Many channel estimation techniques are described by various researchers in MIMO-OFDM system. These techniques are training- based, blind and semi-blind channel estimation techniques [6]. The LS and MMSE are the most popular estimation techniques [2, 3, 4]. The LS estimation has less complexity but at the same time, it has high MSE. The MMSE estimation has less MSE than LS estimation at low values of SNR with more complexity. An Evolutionary Programming-based channel estimation [14] is applied to optimize LS and MMSE estimation. This approach minimizes the MSE more than the LS and MMSE estimation. A better pilot based estimation [12, 13] is developed for fast time varying system to estimate Rayleigh channel complex amplitude (CA) and the carrier frequency offset (CFO). The performance of LS algorithm is enhanced by the optimization of pilot tones using differential evolution algorithm [11] in a new approach. Also sparsity-aware approach of NBI estimation [8] is presented to improve the performance of MIMO-OFDM system.